What is your surname, Alice? If you like the name so much are you sure you're not writing it off for a non reason? I'm trying to think of a surname which would rule it out... Ellis? Alice Ellis is ok...Wallis? Alice Wallis? Again, not a deal breaker. Inwonderland? That could be a problem, I grant you

If it's an issue with the initial could you call her Something Alice Surname, and call her Alice? I know a couple of people whose parents swapped the two first names around to avoid unfortunate acronyms, but used the middle name day to day.